Ecology Lab
Biology 229
1-20-2010
Prof. Kerkhoff
Measuring biodiversity of ecological communities
Biodiversity is one of the primary interests of ecologists, but quantifying the
species diversity of ecological communities is complicated. In addition to issues
of statistical sampling, the rather arbitrary nature of delineating an ecological
community, and the difficulty of positively identifying all of the species present,
species diversity itself has two separate components: 1.) the number of species
present (species richness), and 2.) their relative abundances (termed dominance
or evenness).
As a result, many different measures (or indices) of biodiversity have been
developed, and whole books have been written explaining and comparing them
(Magurran 2004). Here, we will explore two measures of biodiversity: The
Shannon index (Hʼ, also termed the Shannon-Wiener index) and the Simpson
index (D). We will then consider one measure used to compare diversity among
communities, Jaccardʼs similarity index.
Shannon index
The idea behind this index is that the diversity of a community is similar to the
amount of information in a code or message. It is calculated in the following way:
H'= −∑ pi ln pi
where pi is the proportion of individuals found in species i. For a well-sampled
community, we can estimate this proportion as pi = ni/N, where ni is the number
of individuals in species i and N is the total number of individuals in the
community. Since by definition the pis will all be between zero and one, the
€ all of the terms of the summation negative, which is why we
natural log makes
take the inverse of the sum.
Interpretation: Typical values are generally between 1.5 and 3.5 in most
ecological studies, and the index is rarely greater than 4. The Shannon index
increases as both the richness and the evenness of the community increase. The
fact that the index incorporates both components of biodiversity can be seen as
both a strength and a weakness. It is a strength because it provides a simple,
synthetic summary, but it is a weakness because it makes it difficult to compare
communities that differ greatly in richness.
Due to the confounding of richness and evenness in the Shannon index, many
biodiversity researchers prefer to stick to two numbers for comparative studies,
combining a direct estimate of species richness (the total number of species in
the community, S) with some measure of dominance or evenness. The most
common dominance measure is Simpsonʼs index.
Simpsonʼs index
Since evenness and dominance are simply two sides of the same coin, their
measures are complimentary. Simpsonʼs index is based on the probability of any
two individuals drawn at random from an infinitely large community belonging to
the same species:
D = ∑ pi2
where again pi is the proportion of individuals found in species i. For a finite
community, this is
€
D=∑
n i (n i −1)
N(N −1)
Interpretation: Now D is a measure of dominance, so as D increases, diversity (in
the sense of evenness) decreases. Thus, Simpsonʼs index is usually reported as
its complement 1-D (or sometimes 1/D or –lnD). Since D takes on values
between zero and one and approaches one in the limit of a monoculture, (1-D)
provides an intuitive proportional measure of diversity that is much less sensitive
to species richness.
€
Comparing communities: Jaccardʼs index
Of course, we are usually interested not just in the diversity of a single site, but in
comparing biodiversity levels across sites. An intuitive measure of similarity
between two samples can summarize the fraction of species they share.
Jaccardʼs index is the simplest summary of this, taking the following form:
J=
sc
sa + sb + sc
where sa and sb are the numbers of species unique to samples a and b,
respectively, and sc is the number of species common to the two samples.
Interpretation: Jaccardʼs index of similarity is very straightforward since it is
simply the fraction of species shared between the samples. Keep in mind,
however, that Jaccardʼs index only utilizes the richness component of diversity,
€
since it does not entail any information on abundance. As a pairwise measure,
we can examine how Jaccardʼs index varies with the distance or environmental
differences between the sites.
YOUR ASSIGNMENT
1. Having surveyed your tabletop forest, calculate:
a. the species richness (S),
b. Shannon diversity (Hʼ) and
c. Simpsonʼs diversity (1-D) for your sample.
2. In consultation with each of the other groups
a. Compare your samples, based on the different measures of
diversity. Rank the four samples. Do the different measures of
diversity all agree? Explain
b. Calculate Jaccardʼs similarity for each pair of sites. How do they
compare?
REFERENCES
Magurran, A.E. 2004. Meausuring Biological Diversity. Blackwell.